Final answer:
The question is about the characteristics of a regression equation in a sample of twenty-year-old men. The slope, y-intercept, regression equation, and coefficient of determination are important aspects of this regression analysis.
Step-by-step explanation:
The question states that a linear regression of weight on height was performed on a random sample of 200 twenty-year-old men. Based on this information, we can determine the characteristics of the regression equation.
- The value of the slope is the coefficient of the independent variable (height) and represents the change in weight for each one-unit increase in height. To find the slope, you need to refer to the regression equation or the output provided for the regression analysis.
- The value of the y-intercept is the constant term in the regression equation and represents the estimated weight when the independent variable (height) is equal to zero. Like the slope, you need to refer to the regression equation or output to find the y-intercept.
- The regression equation predicts weight based on the height of an individual. It can be written in the form Y = a + bX, where Y represents the predicted weight, X represents the height, a is the y-intercept, and b is the slope. To calculate the predicted weight for someone 68 inches tall, you substitute 68 for X in the regression equation and solve for Y.
- The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient between weight and height is provided as -0.56. The coefficient of determination, denoted as R^2, is the square of the correlation coefficient. It represents the proportion of the variation in the dependent variable (weight) that can be explained by the independent variable (height). To calculate R^2, you square the correlation coefficient (-0.56^2) which results in 0.3136 or 31.36%.